Fans fought in the stands during Saturday’s preseason game in San Francisco between the 49ers and Oakland Raiders. In a separate incident after the game, two men were injured in shootings in the parking lot. (Ben Margot/Associated Press)

The NFL’s chief security officer said Monday that the league will study the circumstances surrounding the fan violence at this past weekend’s preseason game in San Francisco and eventually will take additional steps to safeguard those who attend games.

But the NFL has no immediate plans for new security initiatives at stadiums because the league believes its current policies are generally effective, said Jeffrey Miller, formerly the commissioner of the Pennsylvania state police before joining the NFL in 2008.

“What happened the other night obviously was unacceptable,” Miller said. “We’re still in fact-finding mode. . . . We believe we have a pretty strong program in place. We believe this is an aberration. But we’re going to look at what we can do when we have all the facts. We will do more.”

Two men were injured in shootings in the parking lot after Saturday’s game, and another man reportedly was assaulted and knocked unconscious in a restroom during the game between the San Francisco 49ers and Oakland Raiders.

Authorities in the Bay Area reportedly were investigating whether the shootings might have been related to gang violence.

The 49ers announced Monday that tailgating in the parking lot during games will be banned. Fans must either enter the stadium or leave the parking lots once the game begins. Such a policy won’t necessarily be enacted at all NFL stadiums, Miller said.

Miller said NFL officials were considering the possibility that the violence was “a reflection of societal issues” and added: “Will you see big changes [to security procedures in NFL stadiums] right away because of this? I don’t think so because we have a strong policy in place.”

The NFL instituted a fan code of conduct in stadiums in 2008, enabling officials to eject fans and deny future ticket privileges for abusive actions or impairment from alcohol that results in irresponsible behavior. Miller said one key is for security officers to patrol parking lots before games and identify fans who are drinking excessively and might create problems.

“If you can reduce the number of visibly intoxicated fans who come to your gate, you can eliminate problems early on,” Miller said.

The 49ers also announced they would recommend that their annual preseason matchup with the Raiders be halted at least temporarily.